Mathematics – Differential Geometry
Scientific paper
2005-12-02
Mathematics
Differential Geometry
30 pages 30 pages. in this new version, the standard definition of the Toledo invariant is chosen. Theorem 1.0.5 is slightly s
Scientific paper
We study Hitchin representations and maximal symplectic representations of surface groups, which can be both thought of as generalisations of Fuchsian representations. We show that the corresponding energy functionals are proper on Teichmuller space. We also prove that the mapping class group acts properly on the corresponding moduli spaces. These two results follows from the fact these representations are well displacing which is a consequence they are associated to cross ratios. We state some applications.
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